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73edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-05-06 05:10:29 UTC</tt>.<br>
: The original revision id was <tt>429135632</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=&lt;span style="color: #008909; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;73 tone equal temperament&lt;/span&gt;=


The 73-EDO divides the octave into 73 equal parts of 16.438 cents each. It tempers out 78732/78125 and 262144/253125 in the 5-limit, 126/125 and 245/243 in the 7-limit, 176/175, 441/440 and 4000/3993 in the 11-limit, and 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for [[Starling temperaments#Casablanca%20temperament-Marrakesh|marrakesh temperament]]. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp.
== Theory ==
73edo fits in mavila scale, by the 9;5 relation in the [[7L 2s|superdiatonic]] scheme.
73edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tune it better.


73edo is the 21st [[prime numbers|prime]] edo.</pre></div>
73edo can be used as a tuning of [[trismegistus]] or [[mavila]], by the 9:5 relation in the [[7L 2s|superdiatonic]] scheme, though neither of these use the most accurate 3/2. It is also notable for supporting the 2.3.5.7.13 version of [[sensi]] entirely by patent val.
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;73edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x73 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #008909; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;73 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
=== Prime harmonics ===
&lt;br /&gt;
{{Harmonics in equal|73|intervals=prime}}
The 73-EDO divides the octave into 73 equal parts of 16.438 cents each. It tempers out 78732/78125 and 262144/253125 in the 5-limit, 126/125 and 245/243 in the 7-limit, 176/175, 441/440 and 4000/3993 in the 11-limit, and 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for &lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh"&gt;marrakesh temperament&lt;/a&gt;. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp.&lt;br /&gt;
 
73edo fits in mavila scale, by the 9;5 relation in the &lt;a class="wiki_link" href="/7L%202s"&gt;superdiatonic&lt;/a&gt; scheme.&lt;br /&gt;
=== Subsets and supersets ===
&lt;br /&gt;
73edo is the 21st [[prime edo]], past [[71edo]] and before [[79edo]].
73edo is the 21st &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Intervals ==
{{Interval table}}
 
== Notation ==
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[80edo#Sagittal notation|80-EDO]].
 
==== Evo flavor ====
<imagemap>
File:73-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 719 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[64/63]]
rect 120 80 220 106 [[81/80]]
rect 220 80 350 106 [[45/44]]
rect 350 80 470 106 [[33/32]]
default [[File:73-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:73-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[64/63]]
rect 120 80 220 106 [[81/80]]
rect 220 80 350 106 [[45/44]]
rect 350 80 470 106 [[33/32]]
default [[File:73-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Scales ==
* Porky[7]: 10 10 10 13 10 10 10 ((10, 20, 30, 43, 53, 63, 73)\73)
 
== Instruments ==
 
A [[Lumatone mapping for 73edo]] is available.
 
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/meZYE1Yj2pY ''microtonal improvisation in 73edo''] (2025)
* ''Waltz in 73edo'' (2026)
** [https://www.youtube.com/shorts/sRZEJVBuDl0 ''<nowiki>[short]</nowiki>''] (Lumatone view)
** [https://www.youtube.com/watch?v=Z-3a5LJlul8 ''<nowiki>[full version]</nowiki>'']
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=NuCnLVijULo ''Little Fugue on Happy Birthday''] (2020)
 
[[Category:Marrakesh]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/73edo"